ODE No. 1689

8.99 ODE No. 1689

$x^{4} \frac{d^{2}}{d x^{2}} y (x) + {(x \frac{d}{d x} y (x) - y (x))}^{3} = 0$

Mathematica: cpu = 0.642582 (sec), leaf count = 329 ${{y (x) \to - i x \log (- \frac{\sqrt{- 8 i c_{1} x^{2} - \sinh (2 c_{2}) - \cosh (2 c_{2})}}{4 c_{1} x} - \frac{i \sinh (c_{2})}{4 c_{1} x} - \frac{i \cosh (c_{2})}{4 c_{1} x})}, {y (x) \to - i x \log (- \frac{\sqrt{- 8 i c_{1} x^{2} - \sinh (2 c_{2}) - \cosh (2 c_{2})}}{4 c_{1} x} + \frac{i \sinh (c_{2})}{4 c_{1} x} + \frac{i \cosh (c_{2})}{4 c_{1} x})}, {y (x) \to - i x \log (\frac{\sqrt{- 8 i c_{1} x^{2} - \sinh (2 c_{2}) - \cosh (2 c_{2})}}{4 c_{1} x} - \frac{i \sinh (c_{2})}{4 c_{1} x} - \frac{i \cosh (c_{2})}{4 c_{1} x})}, {y (x) \to - i x \log (\frac{\sqrt{- 8 i c_{1} x^{2} - \sinh (2 c_{2}) - \cosh (2 c_{2})}}{4 c_{1} x} + \frac{i \sinh (c_{2})}{4 c_{1} x} + \frac{i \cosh (c_{2})}{4 c_{1} x})}}$

Maple: cpu = 1.623 (sec), leaf count = 37 ${y (x) = (- \arctan (\frac{1}{\sqrt{_C 1 x^{2} - 1}}) +_C 2) x, y (x) = (\arctan (\frac{1}{\sqrt{_C 1 x^{2} - 1}}) +_C 2) x}$

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